1. Altitude, perpendicular bisector, both, or neither?
Warm-up E A
1. If CD = 3.25, what is BC? B
6.5 G
2. Find AG if DG = 10. D 20 C
3. If CG = 7, find CE?
10.5
Altitude, perpendicular bisector, both, or neither?
PER. BISECTOR
NEITHER
BOTH
ALTITUDE

2. Perpendicular Bisector
perpendicular to a side at its midpoint

3. Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment,
then it is equidistant from the endpoints of the segment

4. How many perpendicular bisectors does a triangle have?
The intersection of the perpendicular bisector is called the CIRCUMCENTER.
How many perpendicular bisectors does a triangle have?

5. What is special about the CIRCUMCENTER?
Equidistant to the vertices of the triangle.

6. Example 1: Point G is the circumcenter of the triangle. Find GB. 7 A 75 2 B C F 7

7. Example 2: Point O is the circumcenter of the triangle. Find CO. 10 A6 B 8 C F 10

8. cuts the angle into 2 equal parts
Angle Bisector
Angle Bisector
cuts the angle into 2 equal parts

9. The intersection of the angle bisectors is called the INCENTER.
How many angle bisectors does a triangle have?

10. What is special about the INCENTER?
Equidistant to sides of the triangle

11. Example 1: Point N is the incenter of the triangle.
Find the length of segment ON. 30 18 18

12. Altitude – the height of the triangle.
(perpendicular to the base.)
Not always inside the triangle.

13. All 3 Altitudes intersect at the Orthocenter.

14. POINTS of CONCURENCY located? In, On, or Out of the triangle
Where are the
POINTS of CONCURENCY located?
In, On, or Out of the triangle
Type of Triangle
Centroid
Incenter
Circumcenter
Orthocenter
ACUTE
OBTUSE
RIGHT

15. orthocenter

16. M A P A C I C O How can I remember all this? Angle Bisector
Perpendicular
Bisector
Median
Altitude
Centroid
Incenter
Circumcenter
Orthocenter